In Birdman there are some techniques for making it all look like a single shot that I've picked up on which are quite obvious, such as the camera turning upwards towards the sky and then having it turn from night to day in a timelapse, but there are other parts where I can't think of how they got it all in one shot (eg. Riggan running through new york in his underwear).
I know I teased this as a comment, but the answer really is disappointing…
They used CGI to mask the transitions.
This doesn't mean it wasn't clever or a lot of hard work by some amazing artists, merely that these days we're quite used to half of humanity vanishing, worlds colliding, or a woman pushing a space ship across galaxies.
Mundane does not mean not clever or incredibly detailed.
Back in the old days, they had to come up with a black frame they could use to cut at, or some of the rather clever physical film-masking techniques, as mentioned in How was the wipe transition done historically? but these days, so long as your lighting matches, you can wipe past a door frame as a character walks through - it's just so easy, relatively speaking.
It does, of course, require great attention to detail so shots do just about match before they reach the edit suite, but the compositing is the job of an artist skilled at masking these joins. You will almost never see them, even frame-by-frame, because of the skill and technology used.
Birdman, in particular, used corners and doors to achieve the cuts. CGI is used to mask the transition almost by making a visually accurate animation to cover the joins.
There is some further exposition in this report on the making of, but nothing too specific - VFX Secrets Behind 'Birdman' Finally Revealed but it does mention that not only the wipes, but also individual scenes were actually digitally composited from several takes.
I often find I'm distracted if I'm watching a movie which has mainly achieved its fame through some kind of technical aspect rather than for its plot and characterisation. I think if you want to watch a movie 'known' for being one continuous shot, then the more recent 1917 is a better bet, from an audience perspective.